import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
%matplotlib inline
from scipy.stats import zscore
import seaborn as sns
from sklearn.cluster import AgglomerativeClustering

Reading the database from excel and seeing at the data¶

veh = pd.read_csv(r'C:\Users\Akash Barwad\Documents\AIML\documents\Project Data\Project-5 - Unsupervised Learning\vehicle-1.csv')

vehtry = pd.read_csv(r'C:\Users\Akash Barwad\Documents\AIML\documents\Project Data\Project-5 - Unsupervised Learning\vehicle-1.csv')

veh.head(30)

veh.columns

Index(['compactness', 'circularity', 'distance_circularity', 'radius_ratio',
       'pr.axis_aspect_ratio', 'max.length_aspect_ratio', 'scatter_ratio',
       'elongatedness', 'pr.axis_rectangularity', 'max.length_rectangularity',
       'scaled_variance', 'scaled_variance.1', 'scaled_radius_of_gyration',
       'scaled_radius_of_gyration.1', 'skewness_about', 'skewness_about.1',
       'skewness_about.2', 'hollows_ratio', 'class'],
      dtype='object')

Understanding the shape and size of the database¶

veh.info()

<class 'pandas.core.frame.DataFrame'>
RangeIndex: 847 entries, 0 to 846
Data columns (total 19 columns):
compactness                    846 non-null float64
circularity                    841 non-null float64
distance_circularity           842 non-null float64
radius_ratio                   840 non-null float64
pr.axis_aspect_ratio           844 non-null float64
max.length_aspect_ratio        846 non-null float64
scatter_ratio                  845 non-null float64
elongatedness                  845 non-null float64
pr.axis_rectangularity         843 non-null float64
max.length_rectangularity      846 non-null float64
scaled_variance                843 non-null float64
scaled_variance.1              844 non-null float64
scaled_radius_of_gyration      844 non-null float64
scaled_radius_of_gyration.1    842 non-null float64
skewness_about                 840 non-null float64
skewness_about.1               845 non-null float64
skewness_about.2               845 non-null float64
hollows_ratio                  846 non-null float64
class                          846 non-null object
dtypes: float64(18), object(1)
memory usage: 125.8+ KB

for feature in veh.columns: # Loop through all columns in the dataframe
    if veh[feature].dtype == 'object': # Only apply for columns with categorical strings
        veh[feature] = pd.Categorical(veh[feature]).codes # Replace strings with an integer

veh.info()

<class 'pandas.core.frame.DataFrame'>
RangeIndex: 847 entries, 0 to 846
Data columns (total 19 columns):
compactness                    846 non-null float64
circularity                    841 non-null float64
distance_circularity           842 non-null float64
radius_ratio                   840 non-null float64
pr.axis_aspect_ratio           844 non-null float64
max.length_aspect_ratio        846 non-null float64
scatter_ratio                  845 non-null float64
elongatedness                  845 non-null float64
pr.axis_rectangularity         843 non-null float64
max.length_rectangularity      846 non-null float64
scaled_variance                843 non-null float64
scaled_variance.1              844 non-null float64
scaled_radius_of_gyration      844 non-null float64
scaled_radius_of_gyration.1    842 non-null float64
skewness_about                 840 non-null float64
skewness_about.1               845 non-null float64
skewness_about.2               845 non-null float64
hollows_ratio                  846 non-null float64
class                          847 non-null int8
dtypes: float64(18), int8(1)
memory usage: 120.0 KB

veh.isnull().values.any()

True

From the above data we assume that the there are null values present in the database also, there are object datatypes which we have taken care of in by changinfg them to integer value.¶

veh.describe().T

veh.shape

(847, 19)

veh.size

16093

sns.pairplot(veh)

C:\Users\Akash Barwad\Anaconda3\lib\site-packages\numpy\lib\histograms.py:824: RuntimeWarning: invalid value encountered in greater_equal
  keep = (tmp_a >= first_edge)
C:\Users\Akash Barwad\Anaconda3\lib\site-packages\numpy\lib\histograms.py:825: RuntimeWarning: invalid value encountered in less_equal
  keep &= (tmp_a <= last_edge)

<seaborn.axisgrid.PairGrid at 0x1e01782ed30>

veh.columns

Index(['compactness', 'circularity', 'distance_circularity', 'radius_ratio',
       'pr.axis_aspect_ratio', 'max.length_aspect_ratio', 'scatter_ratio',
       'elongatedness', 'pr.axis_rectangularity', 'max.length_rectangularity',
       'scaled_variance', 'scaled_variance.1', 'scaled_radius_of_gyration',
       'scaled_radius_of_gyration.1', 'skewness_about', 'skewness_about.1',
       'skewness_about.2', 'hollows_ratio', 'class'],
      dtype='object')

With .describe function we identified that there is presence of outliers. we also checked the same visually with the help of pair plot. now we will see the number of outliers and how they are spread across the database.¶

sns.set(style="whitegrid")
ax = sns.boxplot(x=veh['radius_ratio'],whis=1.5)

sns.set(style="whitegrid")
ax = sns.boxplot(x=veh['pr.axis_aspect_ratio'],whis=1.5)

sns.set(style="whitegrid")
ax = sns.boxplot(x=veh['max.length_aspect_ratio'],whis=1.5)

sns.set(style="whitegrid")
ax = sns.boxplot(x=veh['scaled_variance'],whis=1.5)

sns.set(style="whitegrid")
ax = sns.boxplot(x=veh['scaled_variance.1'],whis=1.5)

sns.set(style="whitegrid")
ax = sns.boxplot(x=veh['scaled_radius_of_gyration.1'],whis=1.5)

sns.set(style="whitegrid")
ax = sns.boxplot(x=veh['skewness_about'],whis=1.5)

Visually also it is confirmed that the outliers are present in the database.¶

veh.mean()

compactness                     93.678487
circularity                     44.828775
distance_circularity            82.110451
radius_ratio                   168.888095
pr.axis_aspect_ratio            61.678910
max.length_aspect_ratio          8.567376
scatter_ratio                  168.901775
elongatedness                   40.933728
pr.axis_rectangularity          20.582444
max.length_rectangularity      147.998818
scaled_variance                188.631079
scaled_variance.1              439.494076
scaled_radius_of_gyration      174.709716
scaled_radius_of_gyration.1     72.447743
skewness_about                   6.364286
skewness_about.1                12.602367
skewness_about.2               188.919527
hollows_ratio                  195.632388
dtype: float64

We will go for the co relation between all the columns also visually with heatmap.¶

cor = veh[['compactness', 'circularity', 'distance_circularity', 'radius_ratio',
       'pr.axis_aspect_ratio', 'max.length_aspect_ratio', 'scatter_ratio',
       'elongatedness', 'pr.axis_rectangularity', 'max.length_rectangularity',
       'scaled_variance', 'scaled_variance.1', 'scaled_radius_of_gyration',
       'scaled_radius_of_gyration.1', 'skewness_about', 'skewness_about.1',
       'skewness_about.2', 'hollows_ratio', 'class']].corr()

cor

sns.heatmap(cor,annot=True,annot_kws={"size": 1.0},cmap='BuPu',vmin=-1,vmax=1)

<matplotlib.axes._subplots.AxesSubplot at 0x1e036d70ac8>

I found this code online to check the presence of outliers and see the exact positions where the outliers are present so tried the same and replaced them with mean values.¶

train = veh

null_columns=train.columns[train.isnull().any()]

train[null_columns].isnull().sum()

compactness                    1
circularity                    6
distance_circularity           5
radius_ratio                   7
pr.axis_aspect_ratio           3
max.length_aspect_ratio        1
scatter_ratio                  2
elongatedness                  2
pr.axis_rectangularity         4
max.length_rectangularity      1
scaled_variance                4
scaled_variance.1              3
scaled_radius_of_gyration      3
scaled_radius_of_gyration.1    5
skewness_about                 7
skewness_about.1               2
skewness_about.2               2
hollows_ratio                  1
class                          1
dtype: int64

print(train[train.isnull().any(axis=1)][null_columns].head())

    compactness  circularity  distance_circularity  radius_ratio  \
5         107.0          NaN                 106.0         172.0   
9          93.0         44.0                  98.0           NaN   
19        101.0         56.0                 100.0         215.0   
35        100.0         46.0                   NaN         172.0   
66         81.0         43.0                  68.0         125.0   

    pr.axis_aspect_ratio  max.length_aspect_ratio  scatter_ratio  \
5                   50.0                      6.0          255.0   
9                   62.0                     11.0          183.0   
19                   NaN                     10.0          208.0   
35                  67.0                      9.0          157.0   
66                  57.0                      8.0          149.0   

    elongatedness  pr.axis_rectangularity  max.length_rectangularity  \
5            26.0                    28.0                      169.0   
9            36.0                    22.0                      146.0   
19           32.0                    24.0                      169.0   
35           43.0                    20.0                      150.0   
66           46.0                    19.0                      146.0   

    scaled_variance  scaled_variance.1  scaled_radius_of_gyration  \
5             280.0              957.0                      264.0   
9             202.0              505.0                      152.0   
19            227.0              651.0                      223.0   
35            170.0              363.0                      184.0   
66            169.0              323.0                      172.0   

    scaled_radius_of_gyration.1  skewness_about  skewness_about.1  \
5                          85.0             5.0               9.0   
9                          64.0             4.0              14.0   
19                         74.0             6.0               5.0   
35                         67.0            17.0               7.0   
66                          NaN             NaN              18.0   

    skewness_about.2  hollows_ratio class  
5              181.0          183.0   bus  
9              195.0          204.0   car  
19             186.0          193.0   car  
35             192.0          200.0   van  
66             179.0          184.0   bus

veh1=veh.fillna(veh.mean())

train = veh1

null_columns=train.columns[train.isnull().any()]

train[null_columns].isnull().sum()

class    1
dtype: int64

print(train[train.isnull().any(axis=1)][null_columns].head())

    class
846   NaN

veh1=veh1.dropna()

veh.shape

(847, 19)

veh1.head(10)

We found out that there are 1-10 number of outliers present in database so we thought to remove them and same has been done with the help of IQR technique. Kindly confirm if this is a good idea in this case or not.¶

Q1 = veh.quantile(0.25)
Q3 = veh.quantile(0.75)
IQR = Q3 - Q1
print(IQR)

compactness                     13.00
circularity                      9.00
distance_circularity            28.00
radius_ratio                    54.00
pr.axis_aspect_ratio             8.00
max.length_aspect_ratio          3.00
scatter_ratio                   51.00
elongatedness                   13.00
pr.axis_rectangularity           4.00
max.length_rectangularity       22.00
scaled_variance                 50.00
scaled_variance.1              269.00
scaled_radius_of_gyration       49.00
scaled_radius_of_gyration.1      8.00
skewness_about                   7.00
skewness_about.1                14.00
skewness_about.2                 9.00
hollows_ratio                   10.75
dtype: float64

print(veh1 < (Q1 - 1.5 * IQR)) 
(veh1 > (Q3 + 1.5 * IQR))

     circularity  class  compactness  distance_circularity  elongatedness  \
0          False  False        False                 False          False   
1          False  False        False                 False          False   
2          False  False        False                 False          False   
3          False  False        False                 False          False   
4          False  False        False                 False          False   
5          False  False        False                 False          False   
6          False  False        False                 False          False   
7          False  False        False                 False          False   
8          False  False        False                 False          False   
9          False  False        False                 False          False   
10         False  False        False                 False          False   
11         False  False        False                 False          False   
12         False  False        False                 False          False   
13         False  False        False                 False          False   
14         False  False        False                 False          False   
15         False  False        False                 False          False   
16         False  False        False                 False          False   
17         False  False        False                 False          False   
18         False  False        False                 False          False   
19         False  False        False                 False          False   
20         False  False        False                 False          False   
21         False  False        False                 False          False   
22         False  False        False                 False          False   
23         False  False        False                 False          False   
24         False  False        False                 False          False   
25         False  False        False                 False          False   
26         False  False        False                 False          False   
27         False  False        False                 False          False   
28         False  False        False                 False          False   
29         False  False        False                 False          False   
..           ...    ...          ...                   ...            ...   
816        False  False        False                 False          False   
817        False  False        False                 False          False   
818        False  False        False                 False          False   
819        False  False        False                 False          False   
820        False  False        False                 False          False   
821        False  False        False                 False          False   
822        False  False        False                 False          False   
823        False  False        False                 False          False   
824        False  False        False                 False          False   
825        False  False        False                 False          False   
826        False  False        False                 False          False   
827        False  False        False                 False          False   
828        False  False        False                 False          False   
829        False  False        False                 False          False   
830        False  False        False                 False          False   
831        False  False        False                 False          False   
832        False  False        False                 False          False   
833        False  False        False                 False          False   
834        False  False        False                 False          False   
835        False  False        False                 False          False   
836        False  False        False                 False          False   
837        False  False        False                 False          False   
838        False  False        False                 False          False   
839        False  False        False                 False          False   
840        False  False        False                 False          False   
841        False  False        False                 False          False   
842        False  False        False                 False          False   
843        False  False        False                 False          False   
844        False  False        False                 False          False   
845        False  False        False                 False          False   

     hollows_ratio  max.length_aspect_ratio  max.length_rectangularity  \
0            False                    False                      False   
1            False                    False                      False   
2            False                    False                      False   
3            False                    False                      False   
4            False                    False                      False   
5            False                    False                      False   
6            False                    False                      False   
7            False                    False                      False   
8            False                    False                      False   
9            False                    False                      False   
10           False                    False                      False   
11           False                    False                      False   
12           False                    False                      False   
13           False                    False                      False   
14           False                    False                      False   
15           False                    False                      False   
16           False                    False                      False   
17           False                    False                      False   
18           False                    False                      False   
19           False                    False                      False   
20           False                    False                      False   
21           False                    False                      False   
22           False                    False                      False   
23           False                    False                      False   
24           False                    False                      False   
25           False                    False                      False   
26           False                    False                      False   
27           False                    False                      False   
28           False                    False                      False   
29           False                    False                      False   
..             ...                      ...                        ...   
816          False                    False                      False   
817          False                    False                      False   
818          False                    False                      False   
819          False                    False                      False   
820          False                    False                      False   
821          False                    False                      False   
822          False                    False                      False   
823          False                    False                      False   
824          False                    False                      False   
825          False                    False                      False   
826          False                    False                      False   
827          False                    False                      False   
828          False                    False                      False   
829          False                    False                      False   
830          False                    False                      False   
831          False                    False                      False   
832          False                    False                      False   
833          False                    False                      False   
834          False                    False                      False   
835          False                    False                      False   
836          False                    False                      False   
837          False                    False                      False   
838          False                    False                      False   
839          False                    False                      False   
840          False                    False                      False   
841          False                    False                      False   
842          False                    False                      False   
843          False                    False                      False   
844          False                    False                      False   
845          False                    False                      False   

     pr.axis_aspect_ratio  pr.axis_rectangularity  radius_ratio  \
0                   False                   False         False   
1                   False                   False         False   
2                   False                   False         False   
3                   False                   False         False   
4                   False                   False         False   
5                   False                   False         False   
6                   False                   False         False   
7                   False                   False         False   
8                   False                   False         False   
9                   False                   False         False   
10                  False                   False         False   
11                  False                   False         False   
12                  False                   False         False   
13                  False                   False         False   
14                  False                   False         False   
15                  False                   False         False   
16                  False                   False         False   
17                  False                   False         False   
18                  False                   False         False   
19                  False                   False         False   
20                  False                   False         False   
21                  False                   False         False   
22                  False                   False         False   
23                  False                   False         False   
24                  False                   False         False   
25                  False                   False         False   
26                  False                   False         False   
27                  False                   False         False   
28                  False                   False         False   
29                  False                   False         False   
..                    ...                     ...           ...   
816                 False                   False         False   
817                 False                   False         False   
818                 False                   False         False   
819                 False                   False         False   
820                 False                   False         False   
821                 False                   False         False   
822                 False                   False         False   
823                 False                   False         False   
824                 False                   False         False   
825                 False                   False         False   
826                 False                   False         False   
827                 False                   False         False   
828                 False                   False         False   
829                 False                   False         False   
830                 False                   False         False   
831                 False                   False         False   
832                 False                   False         False   
833                 False                   False         False   
834                 False                   False         False   
835                 False                   False         False   
836                 False                   False         False   
837                 False                   False         False   
838                 False                   False         False   
839                 False                   False         False   
840                 False                   False         False   
841                 False                   False         False   
842                 False                   False         False   
843                 False                   False         False   
844                 False                   False         False   
845                 False                   False         False   

     scaled_radius_of_gyration  scaled_radius_of_gyration.1  scaled_variance  \
0                        False                        False            False   
1                        False                        False            False   
2                        False                        False            False   
3                        False                        False            False   
4                        False                        False            False   
5                        False                        False            False   
6                        False                        False            False   
7                        False                        False            False   
8                        False                        False            False   
9                        False                        False            False   
10                       False                        False            False   
11                       False                        False            False   
12                       False                        False            False   
13                       False                        False            False   
14                       False                        False            False   
15                       False                        False            False   
16                       False                        False            False   
17                       False                        False            False   
18                       False                        False            False   
19                       False                        False            False   
20                       False                        False            False   
21                       False                        False            False   
22                       False                        False            False   
23                       False                        False            False   
24                       False                        False            False   
25                       False                        False            False   
26                       False                        False            False   
27                       False                        False            False   
28                       False                        False            False   
29                       False                        False            False   
..                         ...                          ...              ...   
816                      False                        False            False   
817                      False                        False            False   
818                      False                        False            False   
819                      False                        False            False   
820                      False                        False            False   
821                      False                        False            False   
822                      False                        False            False   
823                      False                        False            False   
824                      False                        False            False   
825                      False                        False            False   
826                      False                        False            False   
827                      False                        False            False   
828                      False                        False            False   
829                      False                        False            False   
830                      False                        False            False   
831                      False                        False            False   
832                      False                        False            False   
833                      False                        False            False   
834                      False                        False            False   
835                      False                        False            False   
836                      False                        False            False   
837                      False                        False            False   
838                      False                        False            False   
839                      False                        False            False   
840                      False                        False            False   
841                      False                        False            False   
842                      False                        False            False   
843                      False                        False            False   
844                      False                        False            False   
845                      False                        False            False   

     scaled_variance.1  scatter_ratio  skewness_about  skewness_about.1  \
0                False          False           False             False   
1                False          False           False             False   
2                False          False           False             False   
3                False          False           False             False   
4                False          False           False             False   
5                False          False           False             False   
6                False          False           False             False   
7                False          False           False             False   
8                False          False           False             False   
9                False          False           False             False   
10               False          False           False             False   
11               False          False           False             False   
12               False          False           False             False   
13               False          False           False             False   
14               False          False           False             False   
15               False          False           False             False   
16               False          False           False             False   
17               False          False           False             False   
18               False          False           False             False   
19               False          False           False             False   
20               False          False           False             False   
21               False          False           False             False   
22               False          False           False             False   
23               False          False           False             False   
24               False          False           False             False   
25               False          False           False             False   
26               False          False           False             False   
27               False          False           False             False   
28               False          False           False             False   
29               False          False           False             False   
..                 ...            ...             ...               ...   
816              False          False           False             False   
817              False          False           False             False   
818              False          False           False             False   
819              False          False           False             False   
820              False          False           False             False   
821              False          False           False             False   
822              False          False           False             False   
823              False          False           False             False   
824              False          False           False             False   
825              False          False           False             False   
826              False          False           False             False   
827              False          False           False             False   
828              False          False           False             False   
829              False          False           False             False   
830              False          False           False             False   
831              False          False           False             False   
832              False          False           False             False   
833              False          False           False             False   
834              False          False           False             False   
835              False          False           False             False   
836              False          False           False             False   
837              False          False           False             False   
838              False          False           False             False   
839              False          False           False             False   
840              False          False           False             False   
841              False          False           False             False   
842              False          False           False             False   
843              False          False           False             False   
844              False          False           False             False   
845              False          False           False             False   

     skewness_about.2  
0               False  
1               False  
2               False  
3               False  
4               False  
5               False  
6               False  
7               False  
8               False  
9               False  
10              False  
11              False  
12              False  
13              False  
14              False  
15              False  
16              False  
17              False  
18              False  
19              False  
20              False  
21              False  
22              False  
23              False  
24              False  
25              False  
26              False  
27              False  
28              False  
29              False  
..                ...  
816             False  
817             False  
818             False  
819             False  
820             False  
821             False  
822             False  
823             False  
824             False  
825             False  
826             False  
827             False  
828             False  
829             False  
830             False  
831             False  
832             False  
833             False  
834             False  
835             False  
836             False  
837             False  
838             False  
839             False  
840             False  
841             False  
842             False  
843             False  
844             False  
845             False  

[846 rows x 19 columns]

veh1_out = veh1[~((veh < (Q1 - 1.5 * IQR)) |(veh1 > (Q3 + 1.5 * IQR))).any(axis=1)]
veh1_out.shape

C:\Users\Akash Barwad\Anaconda3\lib\site-packages\ipykernel_launcher.py:1: UserWarning: Boolean Series key will be reindexed to match DataFrame index.
  """Entry point for launching an IPython kernel.

(813, 19)

veh2=veh1_out
veh2.shape

(813, 19)

veh1.shape

(846, 19)

PCA part starts from here¶

X = veh2.iloc[:,0:17].values
y = veh2.iloc[:,18].values
from sklearn.preprocessing import StandardScaler

from sklearn.model_selection import train_test_split
X_train, X_test, y_train, y_test = train_test_split(X,y, test_size = 0.3, random_state = 10)

X_train = StandardScaler().fit_transform(X_train)
X_test = StandardScaler().fit_transform(X_test)

cov_matrix = np.cov(X_train.T)
print('Covariance Matrix \n%s', cov_matrix)

e_vals, e_vecs = np.linalg.eig(cov_matrix)

print('Eigenvectors \n%s' %e_vecs)
print('\nEigenvalues \n%s' %e_vals)

Covariance Matrix 
%s [[ 1.00176056  0.67303392  0.79719405  0.73128119  0.14226364  0.4897036
   0.81465354 -0.79265308  0.81656737  0.67471764  0.79852657  0.82081443
   0.58457404 -0.22514708  0.20633538  0.1376959   0.28394189]
 [ 0.67303392  1.00176056  0.79669218  0.6273473   0.15330433  0.56075265
   0.84708563 -0.81675129  0.84343605  0.96151887  0.80216833  0.83752265
   0.92804391  0.0902563   0.16192697 -0.00591522 -0.14006059]
 [ 0.79719405  0.79669218  1.00176056  0.80121117  0.20216171  0.66252609
   0.91277666 -0.91517946  0.90056848  0.78322186  0.88794423  0.89737534
   0.71146759 -0.20436425  0.11929571  0.24828495  0.11139934]
 [ 0.73128119  0.6273473   0.80121117  1.00176056  0.64795189  0.4625814
   0.77366716 -0.8352769   0.74652657  0.56538905  0.77419265  0.76197567
   0.53703184 -0.39555464  0.0393724   0.14745539  0.41265989]
 [ 0.14226364  0.15330433  0.20216171  0.64795189  1.00176056  0.12795773
   0.14163715 -0.25369252  0.10942912  0.08996209  0.15394392  0.12665473
   0.09981121 -0.34707899 -0.09365954 -0.05106815  0.41185533]
 [ 0.4897036   0.56075265  0.66252609  0.4625814   0.12795773  1.00176056
   0.49350662 -0.50157516  0.49276247  0.64732382  0.40420005  0.45577812
   0.39579378 -0.30658716  0.10369878  0.13530406  0.04777365]
 [ 0.81465354  0.84708563  0.91277666  0.77366716  0.14163715  0.49350662
   1.00176056 -0.97625965  0.99167835  0.81639187  0.98011702  0.99829371
   0.80522309  0.03697039  0.08634074  0.19842877 -0.02688949]
 [-0.79265308 -0.81675129 -0.91517946 -0.8352769  -0.25369252 -0.50157516
  -0.97625965  1.00176056 -0.95216357 -0.77621348 -0.96529805 -0.96072489
  -0.76877563  0.05628881 -0.06604732 -0.17390605 -0.07940512]
 [ 0.81656737  0.84343605  0.90056848  0.74652657  0.10942912  0.49276247
   0.99167835 -0.95216357  1.00176056  0.82011071  0.96540125  0.99207234
   0.80223464  0.04842655  0.09371673  0.2002221  -0.04647376]
 [ 0.67471764  0.96151887  0.78322186  0.56538905  0.08996209  0.64732382
   0.81639187 -0.77621348  0.82011071  1.00176056  0.75608407  0.8045637
   0.87080493  0.07830698  0.1605245   0.01560081 -0.13938041]
 [ 0.79852657  0.80216833  0.88794423  0.77419265  0.15394392  0.40420005
   0.98011702 -0.96529805  0.96540125  0.75608407  1.00176056  0.97967948
   0.78872743  0.04994741  0.05986088  0.19665229 -0.00139958]
 [ 0.82081443  0.83752265  0.89737534  0.76197567  0.12665473  0.45577812
   0.99829371 -0.96072489  0.99207234  0.8045637   0.97967948  1.00176056
   0.80209956  0.04576427  0.08921677  0.19065291 -0.02210679]
 [ 0.58457404  0.92804391  0.71146759  0.53703184  0.09981121  0.39579378
   0.80522309 -0.76877563  0.80223464  0.87080493  0.78872743  0.80209956
   1.00176056  0.24308557  0.18186495 -0.04770615 -0.24973902]
 [-0.22514708  0.0902563  -0.20436425 -0.39555464 -0.34707899 -0.30658716
   0.03697039  0.05628881  0.04842655  0.07830698  0.04994741  0.04576427
   0.24308557  1.00176056 -0.07308904 -0.08195419 -0.85140082]
 [ 0.20633538  0.16192697  0.11929571  0.0393724  -0.09365954  0.10369878
   0.08634074 -0.06604732  0.09371673  0.1605245   0.05986088  0.08921677
   0.18186495 -0.07308904  1.00176056 -0.05403233  0.09956892]
 [ 0.1376959  -0.00591522  0.24828495  0.14745539 -0.05106815  0.13530406
   0.19842877 -0.17390605  0.2002221   0.01560081  0.19665229  0.19065291
  -0.04770615 -0.08195419 -0.05403233  1.00176056  0.04995322]
 [ 0.28394189 -0.14006059  0.11139934  0.41265989  0.41185533  0.04777365
  -0.02688949 -0.07940512 -0.04647376 -0.13938041 -0.00139958 -0.02210679
  -0.24973902 -0.85140082  0.09956892  0.04995322  1.00176056]]
Eigenvectors 
[[-2.71334066e-01  1.20206747e-01  4.72154231e-02  1.56869429e-01
   1.58475547e-01  2.65690158e-01  1.46818644e-01  7.71084057e-01
  -3.69533907e-01  4.21180705e-02  1.09454139e-02 -1.48200492e-03
   6.14976978e-02  1.70502068e-03 -1.74269446e-01 -1.39775092e-02
   2.13875903e-02]
 [-2.89453073e-01 -1.32335559e-01  1.88297668e-01 -8.61928654e-02
  -1.41514553e-01 -7.56203706e-02 -4.05039921e-01  4.55234192e-02
  -1.71499347e-02 -2.37742713e-01  4.46787925e-02  5.64420152e-04
   3.97210550e-01  7.36260068e-02  7.77818481e-02  5.28581121e-01
   3.95584643e-01]
 [-3.03078431e-01  6.95116758e-02 -5.16670127e-02  1.10984545e-01
  -1.03423332e-01  1.70823710e-02  1.37979823e-01 -2.73653175e-01
  -3.10049992e-01  4.29663738e-02  7.92187377e-01 -3.18141636e-03
  -1.67763764e-01 -1.24169779e-02  1.19153679e-01 -4.25671379e-02
   1.16427516e-01]
 [-2.63706299e-01  2.91968978e-01 -6.67524803e-02 -2.09077432e-01
   8.68730517e-02 -1.42276142e-01  1.55358226e-01 -5.71601300e-02
  -1.27533366e-01 -8.36735789e-02 -1.71654390e-01 -2.20712094e-02
   4.74830955e-01  2.65488997e-03  5.71407945e-01 -3.59815169e-01
  -8.47766265e-02]
 [-7.37773033e-02  3.67938167e-01  2.29725370e-03 -5.67716703e-01
  -3.07225177e-03 -5.73252255e-01  1.03782695e-01  1.80855176e-01
  -2.31535187e-03 -4.28430629e-02  6.42184336e-02  1.53979490e-02
  -2.73637481e-01 -5.65001751e-03 -2.42000579e-01  1.58376247e-01
  -2.26949031e-03]
 [-1.91234203e-01  9.68387083e-02  1.60851706e-01  2.29558968e-01
  -7.37216108e-01 -8.70996667e-02  3.66572597e-01  6.63124514e-02
   1.80697116e-01  3.06358154e-01 -1.95832637e-01 -1.41529397e-02
  -1.71217086e-02 -8.78861418e-03  7.85951571e-02  1.17677014e-01
   1.34698237e-02]
 [-3.14059300e-01 -5.54204246e-02 -1.02201955e-01  7.48961011e-03
   1.04371760e-01  6.87282573e-02  1.04975265e-01 -9.83830054e-02
   1.38874968e-01 -9.46739107e-02 -1.33719376e-01  7.90684389e-01
  -8.83247139e-02 -3.90127797e-01 -6.87734039e-02 -1.09386405e-02
   1.23755686e-01]
 [ 3.10312677e-01 -1.98298916e-02  9.58321540e-02  5.41173141e-02
  -9.63851994e-02 -4.36229356e-02 -1.21773639e-01  2.17406591e-01
  -2.68289765e-01 -1.65361829e-01 -2.08532507e-02  2.16251414e-01
  -3.80946143e-01 -1.01813325e-01  6.24411197e-01  2.82983096e-01
  -2.14323735e-01]
 [-3.11202402e-01 -6.97107118e-02 -9.59237500e-02  3.04579514e-02
   9.79151902e-02  8.30312398e-02  9.55092317e-02 -4.64223785e-02
   9.31880281e-02 -2.26122244e-01 -2.41548706e-01 -6.39116137e-03
  -4.49147565e-01  6.76425368e-01  1.44240292e-01 -6.88872185e-02
   2.39516975e-01]
 [-2.81592469e-01 -1.34679728e-01  2.00715657e-01 -4.24900544e-03
  -2.56065087e-01 -3.70767252e-02 -3.58095026e-01  2.09838319e-01
   3.13223856e-01 -3.60480787e-01  1.95863032e-01 -1.58020767e-02
  -8.37822979e-02 -3.01827069e-02 -5.76030199e-02 -3.91511099e-01
  -4.38014739e-01]
 [-3.05708718e-01 -4.77536591e-02 -1.41685198e-01 -2.85197784e-02
   1.96085454e-01  9.20427282e-02  8.71606302e-02 -1.40979826e-01
   6.09093940e-02  1.74861390e-01  1.36289234e-02  3.02141048e-02
   1.08659709e-01  2.00403100e-01 -2.30730579e-02  4.98698066e-01
  -6.87309593e-01]
 [-3.11320875e-01 -6.02537289e-02 -1.03359238e-01  7.38624496e-03
   1.46124477e-01  9.57476906e-02  7.96132592e-02 -6.27871751e-02
   1.02687102e-01 -1.55915806e-01 -1.83821724e-01 -5.70095660e-01
  -2.86753869e-01 -5.75915444e-01  1.17926950e-01  1.46366254e-01
   7.08557316e-02]
 [-2.69016134e-01 -2.16682502e-01  1.81864622e-01 -1.39812035e-01
   1.70075325e-02 -1.11930092e-01 -4.37269108e-01 -1.12415272e-01
  -3.60805608e-01  5.89248604e-01 -2.36427094e-01  8.10031788e-03
  -1.97008163e-01 -3.57841834e-02  9.04672147e-03 -1.94389450e-01
  -8.83089314e-03]
 [ 2.06404871e-02 -5.66522966e-01 -1.11528140e-01 -1.75349911e-01
   1.73505003e-01 -1.99603915e-01  2.04703903e-01  3.45098649e-01
   3.71454709e-01  3.08049985e-01  2.62069939e-01 -3.99176656e-03
   5.64946942e-02  9.02679894e-03  2.84166017e-01 -3.15759970e-02
   1.33815633e-01]
 [-4.35973104e-02  8.89043886e-03  6.14681090e-01  4.63293973e-01
   4.12625798e-01 -4.38418103e-01  1.69523810e-01 -9.13245419e-02
   4.89388310e-02 -4.95654928e-02 -9.74496146e-03 -2.38130513e-03
   9.92048861e-03  3.59376434e-03 -1.36512185e-02  1.27234617e-02
  -2.41899815e-02]
 [-5.30383731e-02  7.11267981e-02 -6.32336972e-01  5.11756978e-01
  -1.45407103e-02 -4.85843815e-01 -2.78261056e-01  1.11102508e-01
  -1.73627773e-02  2.20742869e-02 -4.26012907e-02 -9.46194076e-03
   3.17231746e-02 -2.24330447e-03 -2.40955338e-02 -7.81677734e-03
   2.79377806e-03]
 [-1.50704330e-02  5.72531420e-01  7.89911669e-02  7.28168687e-02
   1.92644530e-01  2.31930785e-01 -3.31138328e-01  9.34557057e-02
   4.84694543e-01  3.46181931e-01  1.51311729e-01  2.69646176e-02
  -1.04136875e-01  7.61882691e-03  2.08214508e-01  5.33027921e-02
   1.25133232e-01]]

Eigenvalues 
[9.70498964e+00 2.58145261e+00 1.19948501e+00 1.14331327e+00
 8.64368272e-01 6.55185311e-01 3.17786946e-01 2.17864457e-01
 1.00304855e-01 7.41329330e-02 5.93348695e-02 3.35072789e-04
 3.57053557e-02 8.35195971e-03 2.69815257e-02 1.85471577e-02
 2.17903391e-02]

tot = sum(e_vals)
var_exp = [( i /tot ) * 100 for i in sorted(e_vals, reverse=True)]
cum_var_exp = np.cumsum(var_exp)
print("Cumulative Variance Explained", cum_var_exp)

Cumulative Variance Explained [ 56.98784364  72.14617179  79.1895656   85.90311813  90.97870149
  94.82595939  96.69200907  97.97131241  98.56030401  98.9956137
  99.34402893  99.55369131  99.71212723  99.84008043  99.94898962
  99.99803245 100.        ]

# Ploting 
plt.figure(figsize=(10 , 5))
plt.bar(range(1, e_vals.size + 1), var_exp, alpha = 0.5, align = 'center', label = 'Individual explained variance')
plt.step(range(1, e_vals.size + 1), cum_var_exp, where='mid', label = 'Cumulative explained variance')
plt.ylabel('Explained Variance Ratio')
plt.xlabel('Principal Components')
plt.legend(loc = 'best')
plt.tight_layout()
plt.show()

eigen_pairs = [(np.abs(e_vals[i]), e_vecs[:,i]) for i in range(len(e_vals))]
eigen_pairs.sort(reverse=True)
eigen_pairs[:7]

[(9.70498963897293,
  array([-0.27133407, -0.28945307, -0.30307843, -0.2637063 , -0.0737773 ,
         -0.1912342 , -0.3140593 ,  0.31031268, -0.3112024 , -0.28159247,
         -0.30570872, -0.31132088, -0.26901613,  0.02064049, -0.04359731,
         -0.05303837, -0.01507043])),
 (2.5814526100817123,
  array([ 0.12020675, -0.13233556,  0.06951168,  0.29196898,  0.36793817,
          0.09683871, -0.05542042, -0.01982989, -0.06971071, -0.13467973,
         -0.04775366, -0.06025373, -0.2166825 , -0.56652297,  0.00889044,
          0.0711268 ,  0.57253142])),
 (1.1994850051042234,
  array([ 0.04721542,  0.18829767, -0.05166701, -0.06675248,  0.00229725,
          0.16085171, -0.10220196,  0.09583215, -0.09592375,  0.20071566,
         -0.1416852 , -0.10335924,  0.18186462, -0.11152814,  0.61468109,
         -0.63233697,  0.07899117])),
 (1.1433132684759448,
  array([ 0.15686943, -0.08619287,  0.11098454, -0.20907743, -0.5677167 ,
          0.22955897,  0.00748961,  0.05411731,  0.03045795, -0.00424901,
         -0.02851978,  0.00738624, -0.13981203, -0.17534991,  0.46329397,
          0.51175698,  0.07281687])),
 (0.8643682716555754,
  array([ 0.15847555, -0.14151455, -0.10342333,  0.08687305, -0.00307225,
         -0.73721611,  0.10437176, -0.0963852 ,  0.09791519, -0.25606509,
          0.19608545,  0.14612448,  0.01700753,  0.173505  ,  0.4126258 ,
         -0.01454071,  0.19264453])),
 (0.6551853108346146,
  array([ 0.26569016, -0.07562037,  0.01708237, -0.14227614, -0.57325226,
         -0.08709967,  0.06872826, -0.04362294,  0.08303124, -0.03707673,
          0.09204273,  0.09574769, -0.11193009, -0.19960392, -0.4384181 ,
         -0.48584381,  0.23193079])),
 (0.3177869464997268,
  array([ 0.14681864, -0.40503992,  0.13797982,  0.15535823,  0.10378269,
          0.3665726 ,  0.10497526, -0.12177364,  0.09550923, -0.35809503,
          0.08716063,  0.07961326, -0.43726911,  0.2047039 ,  0.16952381,
         -0.27826106, -0.33113833]))]

w = np.hstack((eigen_pairs[0][1].reshape(17,1), 
                      eigen_pairs[1][1].reshape(17,1)))
print('Matrix W:\n', w)
X_pca = X_train.dot(w)

Matrix W:
 [[-0.27133407  0.12020675]
 [-0.28945307 -0.13233556]
 [-0.30307843  0.06951168]
 [-0.2637063   0.29196898]
 [-0.0737773   0.36793817]
 [-0.1912342   0.09683871]
 [-0.3140593  -0.05542042]
 [ 0.31031268 -0.01982989]
 [-0.3112024  -0.06971071]
 [-0.28159247 -0.13467973]
 [-0.30570872 -0.04775366]
 [-0.31132088 -0.06025373]
 [-0.26901613 -0.2166825 ]
 [ 0.02064049 -0.56652297]
 [-0.04359731  0.00889044]
 [-0.05303837  0.0711268 ]
 [-0.01507043  0.57253142]]

X_train.shape, w.shape, X_pca.shape

((569, 17), (17, 2), (569, 2))

X_pca

array([[-3.17335885, -0.65924239],
       [-1.61895414,  0.70052913],
       [ 5.05334739, -1.95490136],
       ...,
       [ 0.08009224,  0.78708036],
       [ 2.45561652,  1.15162265],
       [ 1.71599444,  2.68719083]])

Confirmed the code with SVM.¶

from sklearn.svm import SVC
from sklearn.model_selection import train_test_split

clf = SVC()
clf.fit(X_train, y_train)
print ('score', clf.score(X_test, y_test))

score 0.9672131147540983

	count	mean	std	min	25%	50%	75%	max
compactness	846.0	93.678487	8.234474	73.0	87.00	93.0	100.0	119.0
circularity	841.0	44.828775	6.152172	33.0	40.00	44.0	49.0	59.0
distance_circularity	842.0	82.110451	15.778292	40.0	70.00	80.0	98.0	112.0
radius_ratio	840.0	168.888095	33.520198	104.0	141.00	167.0	195.0	333.0
pr.axis_aspect_ratio	844.0	61.678910	7.891463	47.0	57.00	61.0	65.0	138.0
max.length_aspect_ratio	846.0	8.567376	4.601217	2.0	7.00	8.0	10.0	55.0
scatter_ratio	845.0	168.901775	33.214848	112.0	147.00	157.0	198.0	265.0
elongatedness	845.0	40.933728	7.816186	26.0	33.00	43.0	46.0	61.0
pr.axis_rectangularity	843.0	20.582444	2.592933	17.0	19.00	20.0	23.0	29.0
max.length_rectangularity	846.0	147.998818	14.515652	118.0	137.00	146.0	159.0	188.0
scaled_variance	843.0	188.631079	31.411004	130.0	167.00	179.0	217.0	320.0
scaled_variance.1	844.0	439.494076	176.666903	184.0	318.00	363.5	587.0	1018.0
scaled_radius_of_gyration	844.0	174.709716	32.584808	109.0	149.00	173.5	198.0	268.0
scaled_radius_of_gyration.1	842.0	72.447743	7.486190	59.0	67.00	71.5	75.0	135.0
skewness_about	840.0	6.364286	4.920649	0.0	2.00	6.0	9.0	22.0
skewness_about.1	845.0	12.602367	8.936081	0.0	5.00	11.0	19.0	41.0
skewness_about.2	845.0	188.919527	6.155809	176.0	184.00	188.0	193.0	206.0
hollows_ratio	846.0	195.632388	7.438797	181.0	190.25	197.0	201.0	211.0

	compactness	circularity	distance_circularity	radius_ratio	pr.axis_aspect_ratio	max.length_aspect_ratio	scatter_ratio	elongatedness	pr.axis_rectangularity	max.length_rectangularity	scaled_variance	scaled_variance.1	scaled_radius_of_gyration	scaled_radius_of_gyration.1	skewness_about	skewness_about.1	skewness_about.2	hollows_ratio	class
compactness	1.000000	0.689786	0.791707	0.691081	0.091779	0.148249	0.812770	-0.788736	0.814248	0.676143	0.764361	0.818674	0.585845	-0.250603	0.236685	0.157670	0.298528	0.365552	-0.033796
circularity	0.689786	1.000000	0.797180	0.625051	0.154283	0.251407	0.858265	-0.827246	0.856603	0.965729	0.806791	0.850863	0.935950	0.053080	0.144968	-0.011869	-0.106339	0.045652	-0.160546
distance_circularity	0.791707	0.797180	1.000000	0.771748	0.158684	0.264621	0.907949	-0.913020	0.896273	0.775149	0.865710	0.890541	0.706950	-0.227001	0.114665	0.266049	0.146027	0.333648	-0.065209
radius_ratio	0.691081	0.625051	0.771748	1.000000	0.665363	0.450486	0.738480	-0.792946	0.712744	0.571083	0.798294	0.725598	0.541325	-0.181520	0.049112	0.174469	0.382912	0.472339	-0.182921
pr.axis_aspect_ratio	0.091779	0.154283	0.158684	0.665363	1.000000	0.648861	0.103832	-0.183492	0.079566	0.127322	0.273738	0.089750	0.122454	0.152860	-0.058539	-0.032180	0.240201	0.267760	-0.098431
max.length_aspect_ratio	0.148249	0.251407	0.264621	0.450486	0.648861	1.000000	0.165998	-0.180053	0.161603	0.305943	0.319033	0.143745	0.189752	0.295638	0.015446	0.043491	-0.026184	0.143919	0.207619
scatter_ratio	0.812770	0.858265	0.907949	0.738480	0.103832	0.165998	1.000000	-0.973504	0.992078	0.810017	0.951672	0.996328	0.800577	-0.028006	0.074376	0.213512	0.005171	0.118504	-0.288904
elongatedness	-0.788736	-0.827246	-0.913020	-0.792946	-0.183492	-0.180053	-0.973504	1.000000	-0.950405	-0.776150	-0.938313	-0.956488	-0.766671	0.103535	-0.052243	-0.186027	-0.114846	-0.216769	0.339348
pr.axis_rectangularity	0.814248	0.856603	0.896273	0.712744	0.079566	0.161603	0.992078	-0.950405	1.000000	0.813135	0.938182	0.992316	0.798522	-0.015711	0.083219	0.215200	-0.019066	0.099481	-0.259102
max.length_rectangularity	0.676143	0.965729	0.775149	0.571083	0.127322	0.305943	0.810017	-0.776150	0.813135	1.000000	0.746657	0.797485	0.866554	0.041283	0.136077	0.001660	-0.104437	0.076770	-0.032399
scaled_variance	0.764361	0.806791	0.865710	0.798294	0.273738	0.319033	0.951672	-0.938313	0.938182	0.746657	1.000000	0.949766	0.781016	0.112452	0.036165	0.196202	0.014434	0.086708	-0.312836
scaled_variance.1	0.818674	0.850863	0.890541	0.725598	0.089750	0.143745	0.996328	-0.956488	0.992316	0.797485	0.949766	1.000000	0.797318	-0.016642	0.077288	0.202398	0.006648	0.103839	-0.288146
scaled_radius_of_gyration	0.585845	0.935950	0.706950	0.541325	0.122454	0.189752	0.800577	-0.766671	0.798522	0.866554	0.781016	0.797318	1.000000	0.192245	0.166785	-0.056067	-0.225882	-0.118597	-0.250967
scaled_radius_of_gyration.1	-0.250603	0.053080	-0.227001	-0.181520	0.152860	0.295638	-0.028006	0.103535	-0.015711	0.041283	0.112452	-0.016642	0.192245	1.000000	-0.088736	-0.126686	-0.752437	-0.804793	-0.213049
skewness_about	0.236685	0.144968	0.114665	0.049112	-0.058539	0.015446	0.074376	-0.052243	0.083219	0.136077	0.036165	0.077288	0.166785	-0.088736	1.000000	-0.035154	0.115728	0.097293	0.119652
skewness_about.1	0.157670	-0.011869	0.266049	0.174469	-0.032180	0.043491	0.213512	-0.186027	0.215200	0.001660	0.196202	0.202398	-0.056067	-0.126686	-0.035154	1.000000	0.077460	0.205115	-0.010674
skewness_about.2	0.298528	-0.106339	0.146027	0.382912	0.240201	-0.026184	0.005171	-0.114846	-0.019066	-0.104437	0.014434	0.006648	-0.225882	-0.752437	0.115728	0.077460	1.000000	0.893869	0.067251
hollows_ratio	0.365552	0.045652	0.333648	0.472339	0.267760	0.143919	0.118504	-0.216769	0.099481	0.076770	0.086708	0.103839	-0.118597	-0.804793	0.097293	0.205115	0.893869	1.000000	0.235874
class	-0.033796	-0.160546	-0.065209	-0.182921	-0.098431	0.207619	-0.288904	0.339348	-0.259102	-0.032399	-0.312836	-0.288146	-0.250967	-0.213049	0.119652	-0.010674	0.067251	0.235874	1.000000

	compactness	circularity	distance_circularity	radius_ratio	pr.axis_aspect_ratio	max.length_aspect_ratio	scatter_ratio	elongatedness	pr.axis_rectangularity	max.length_rectangularity	scaled_variance	scaled_variance.1	scaled_radius_of_gyration	scaled_radius_of_gyration.1	skewness_about	skewness_about.1	skewness_about.2	hollows_ratio	class
0	95.0	48.0	83.0	178.0	72.0	10.0	162.0	42.0	20.0	159.0	176.0	379.0	184.0	70.0	6.0	16.0	187.0	197.0	van
1	91.0	41.0	84.0	141.0	57.0	9.0	149.0	45.0	19.0	143.0	170.0	330.0	158.0	72.0	9.0	14.0	189.0	199.0	van
2	104.0	50.0	106.0	209.0	66.0	10.0	207.0	32.0	23.0	158.0	223.0	635.0	220.0	73.0	14.0	9.0	188.0	196.0	car
3	93.0	41.0	82.0	159.0	63.0	9.0	144.0	46.0	19.0	143.0	160.0	309.0	127.0	63.0	6.0	10.0	199.0	207.0	van
4	85.0	44.0	70.0	205.0	103.0	52.0	149.0	45.0	19.0	144.0	241.0	325.0	188.0	127.0	9.0	11.0	180.0	183.0	bus
5	107.0	NaN	106.0	172.0	50.0	6.0	255.0	26.0	28.0	169.0	280.0	957.0	264.0	85.0	5.0	9.0	181.0	183.0	bus
6	97.0	43.0	73.0	173.0	65.0	6.0	153.0	42.0	19.0	143.0	176.0	361.0	172.0	66.0	13.0	1.0	200.0	204.0	bus
7	90.0	43.0	66.0	157.0	65.0	9.0	137.0	48.0	18.0	146.0	162.0	281.0	164.0	67.0	3.0	3.0	193.0	202.0	van
8	86.0	34.0	62.0	140.0	61.0	7.0	122.0	54.0	17.0	127.0	141.0	223.0	112.0	64.0	2.0	14.0	200.0	208.0	van
9	93.0	44.0	98.0	NaN	62.0	11.0	183.0	36.0	22.0	146.0	202.0	505.0	152.0	64.0	4.0	14.0	195.0	204.0	car
10	86.0	36.0	70.0	143.0	61.0	9.0	133.0	50.0	18.0	130.0	153.0	266.0	127.0	66.0	2.0	10.0	194.0	202.0	van
11	90.0	34.0	66.0	136.0	55.0	6.0	123.0	54.0	17.0	118.0	148.0	224.0	118.0	65.0	5.0	26.0	196.0	202.0	car
12	88.0	46.0	74.0	171.0	68.0	6.0	152.0	43.0	19.0	148.0	180.0	349.0	192.0	71.0	5.0	11.0	189.0	195.0	bus
13	89.0	42.0	85.0	144.0	58.0	10.0	152.0	44.0	19.0	144.0	173.0	345.0	161.0	72.0	8.0	13.0	187.0	197.0	van
14	94.0	49.0	79.0	203.0	71.0	5.0	174.0	37.0	21.0	154.0	196.0	465.0	206.0	71.0	6.0	2.0	197.0	199.0	bus
15	96.0	55.0	103.0	201.0	65.0	9.0	204.0	32.0	23.0	166.0	227.0	624.0	246.0	74.0	6.0	2.0	186.0	194.0	car
16	89.0	36.0	51.0	109.0	52.0	6.0	118.0	57.0	17.0	129.0	137.0	206.0	125.0	80.0	2.0	14.0	181.0	185.0	van
17	99.0	41.0	77.0	197.0	69.0	6.0	177.0	36.0	21.0	139.0	202.0	485.0	151.0	72.0	4.0	10.0	198.0	199.0	bus
18	104.0	54.0	100.0	186.0	61.0	10.0	216.0	31.0	24.0	173.0	225.0	686.0	220.0	74.0	5.0	11.0	185.0	195.0	car
19	101.0	56.0	100.0	215.0	NaN	10.0	208.0	32.0	24.0	169.0	227.0	651.0	223.0	74.0	6.0	5.0	186.0	193.0	car
20	84.0	47.0	75.0	153.0	64.0	6.0	154.0	43.0	19.0	145.0	175.0	354.0	184.0	75.0	0.0	3.0	185.0	192.0	bus
21	84.0	37.0	53.0	121.0	59.0	5.0	123.0	55.0	17.0	125.0	141.0	221.0	133.0	82.0	7.0	1.0	179.0	183.0	van
22	94.0	43.0	64.0	173.0	69.0	7.0	150.0	43.0	19.0	142.0	169.0	344.0	177.0	68.0	9.0	1.0	199.0	206.0	bus
23	87.0	39.0	70.0	148.0	61.0	7.0	143.0	46.0	18.0	136.0	164.0	307.0	141.0	69.0	1.0	2.0	192.0	199.0	bus
24	99.0	53.0	105.0	219.0	66.0	11.0	204.0	32.0	23.0	165.0	221.0	623.0	224.0	68.0	0.0	6.0	191.0	201.0	car
25	85.0	45.0	80.0	154.0	64.0	9.0	147.0	45.0	19.0	148.0	169.0	324.0	174.0	71.0	1.0	4.0	188.0	199.0	van
26	83.0	36.0	54.0	119.0	57.0	6.0	128.0	53.0	18.0	125.0	143.0	238.0	139.0	82.0	6.0	3.0	179.0	183.0	car
27	107.0	54.0	98.0	203.0	65.0	11.0	218.0	31.0	25.0	167.0	229.0	696.0	216.0	72.0	1.0	28.0	187.0	199.0	car
28	102.0	45.0	85.0	193.0	64.0	6.0	192.0	33.0	22.0	146.0	217.0	570.0	163.0	76.0	6.0	7.0	195.0	193.0	bus
29	80.0	38.0	63.0	129.0	55.0	7.0	146.0	46.0	19.0	130.0	168.0	314.0	158.0	83.0	9.0	20.0	180.0	185.0	car

	compactness	circularity	distance_circularity	radius_ratio	pr.axis_aspect_ratio	max.length_aspect_ratio	scatter_ratio	elongatedness	pr.axis_rectangularity	max.length_rectangularity	scaled_variance	scaled_variance.1	scaled_radius_of_gyration	scaled_radius_of_gyration.1	skewness_about	skewness_about.1	skewness_about.2	hollows_ratio	class
0	95.0	48.000000	83.0	178.000000	72.0	10.0	162.0	42.0	20.0	159.0	176.0	379.0	184.0	70.0	6.0	16.0	187.0	197.0	van
1	91.0	41.000000	84.0	141.000000	57.0	9.0	149.0	45.0	19.0	143.0	170.0	330.0	158.0	72.0	9.0	14.0	189.0	199.0	van
2	104.0	50.000000	106.0	209.000000	66.0	10.0	207.0	32.0	23.0	158.0	223.0	635.0	220.0	73.0	14.0	9.0	188.0	196.0	car
3	93.0	41.000000	82.0	159.000000	63.0	9.0	144.0	46.0	19.0	143.0	160.0	309.0	127.0	63.0	6.0	10.0	199.0	207.0	van
4	85.0	44.000000	70.0	205.000000	103.0	52.0	149.0	45.0	19.0	144.0	241.0	325.0	188.0	127.0	9.0	11.0	180.0	183.0	bus
5	107.0	44.828775	106.0	172.000000	50.0	6.0	255.0	26.0	28.0	169.0	280.0	957.0	264.0	85.0	5.0	9.0	181.0	183.0	bus
6	97.0	43.000000	73.0	173.000000	65.0	6.0	153.0	42.0	19.0	143.0	176.0	361.0	172.0	66.0	13.0	1.0	200.0	204.0	bus
7	90.0	43.000000	66.0	157.000000	65.0	9.0	137.0	48.0	18.0	146.0	162.0	281.0	164.0	67.0	3.0	3.0	193.0	202.0	van
8	86.0	34.000000	62.0	140.000000	61.0	7.0	122.0	54.0	17.0	127.0	141.0	223.0	112.0	64.0	2.0	14.0	200.0	208.0	van
9	93.0	44.000000	98.0	168.888095	62.0	11.0	183.0	36.0	22.0	146.0	202.0	505.0	152.0	64.0	4.0	14.0	195.0	204.0	car

	circularity	class	compactness	distance_circularity	elongatedness	hollows_ratio	max.length_aspect_ratio	max.length_rectangularity	pr.axis_aspect_ratio	pr.axis_rectangularity	radius_ratio	scaled_radius_of_gyration	scaled_radius_of_gyration.1	scaled_variance	scaled_variance.1	scatter_ratio	skewness_about	skewness_about.1	skewness_about.2
0	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False
1	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False
2	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False
3	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False
4	False	False	False	False	False	False	True	False	True	False	False	False	True	False	False	False	False	False	False
5	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False
6	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False
7	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False
8	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False
9	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False
10	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False
11	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False
12	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False
13	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False
14	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False
15	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False
16	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False
17	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False
18	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False
19	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False
20	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False
21	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False
22	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False
23	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False
24	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False
25	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False
26	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False
27	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False
28	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False
29	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False
...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
816	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False
817	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False
818	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False
819	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False
820	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False
821	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False
822	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False
823	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False
824	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False
825	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False
826	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False
827	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False
828	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False
829	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False
830	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False
831	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False
832	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False
833	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False
834	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False
835	False	False	False	False	False	False	False	False	False	False	False	False	False	False	True	False	False	False	False
836	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False
837	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False
838	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False
839	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False
840	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False
841	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False
842	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False
843	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False
844	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False
845	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False	False